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Adding and Subtracting Surds

Adding and Subtracting Surds

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Adding and Subtracting Surds

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  1. Adding and Subtracting Surds Slideshow 8, Mr Richard Sasaki, Room 307

  2. Objectives • Be able to convert numbers in index form into fractions and surds • Understand the values of surds that cannot be simplified • Be able to add and subtract surds together

  3. Index Form • Let’s review some rules about index form. • Writing numbers in surd form can help us simplify them further.

  4. Index Form • Examples • Write in surd form. • Write in surd form. • Just try to remember that and . If is a surd then the denominator must be changed to an integer.

  5. Simplifying Surds • Surds are often in the form… • Radicand • If is in its simplest form, what values can take? • 10, • 6, • 5, • 2, • 3, • 7, • … • These are the numbers that do not have square factors (other than 1).

  6. Answers

  7. Adding and Subtracting Surds • Example • How can we simplify ? • If the radicands are the same, we can easily add roots together. Simplify • If there are fractions, we need to make the denominators the same too.

  8. Adding and Subtracting Surds • Example • How can we simplify ? • If the radicands are the same, we can easily add roots together. Simplify • If there are fractions, we need to make the denominators the same too.

  9. Adding and Subtracting Surds • Example • Can we simplify ? • No we can’t. Both and are in their simplest forms. So we just leave it the same. Simplify

  10. Answers • Let . • . • This is one method… • But . • . • or

  11. Answers • and • and The radicand multiplied by 100 gives the same result multiplied by 10. (i.e if . to 3 s.f each.